We conclude this introduction by recording Hausdorff measure
counterparts to Theorems REF ,
REF , and REF . These are, respectively, Theorems REF , REF , and REF . Theorems REF  and
REF  can be obtained as a simple consequence of
combining the relevant Lebesgue measure statement (in our case,
Theorem REF  or REF ) with [1]}. The latter statement, appearing below as Theorem
AB, is essentially a general “transference principle,” proved by the
first author and Beresnevich, which allows us to more-or-less
immediately read off a Hausdorff measure analogue when given an
appropriate Lebesgue measure Khintchine–Groshev type
statement. Theorem AB is a consequence of the mass transference
principle for systems of linear forms [1]} which, informally speaking, allows us to transfer
Lebesgue measure statements for limsup sets determined by
neighbourhoods of planes (i.e. systems of linear forms) to Hausdorff
measure statements. The mass transference principle for systems of
linear forms is just one natural generalization of the original
mass transference principle due to Beresnevich and Velani
[3]}.
